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problem #274 - posted wednesday, march 26, 2008

 
Factorialus Sum Consecutivos.

Okay, I don't know Latin. But I do know that 5! = 120 = 39 + 40 + 41 .
 
a) How many ways can 5! be written as a sum of (two or more)
consecutive positive integers? (s.c.p.i.)
 
b) Describe a procedure to count the number of ways that any
given natural number, m, can be expressed as the s.c.p.i.
 
c) Exactly how many ways can 74 factorial (74!) be written as
the sum of consecutive positive integers (s.c.p.i.)?
 

Show your steps, formulas, and reasoning; one point penalty for resubmissions.
.
Big Book of
Factorials
 
deadline is thursday, april 3, 2008 by Midnight Pacific Time USA
(GMT 8:00) or until this page is updated. See rules below.
(c) 1997-2008 Dan Bach and B & L Math Enterprises; all rights reserved. Download for personal use only.
 
 
 
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Claudio Baiocchi . . . . . . 7
Etienne Desclin . . . . . . . 7
Tim Poe . . . . . . . . . . . . . 7
Philippe Fondanaiche . 6
James Laverty. . . . . . . . 6
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2. Nick McGrath (2) . . . . . 798
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4. Phil Sayre (4) . . . . . . . . 540
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20. Kirk Bresniker (20) . . 163
 
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22. Philippe Fondanaiche (23) . 160
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26. Joe Alvord (26) . . . . . . . . . . 136
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28. Radu Ionescu (28) . . . . . . . . 133
29. Anirban Bhattacharyya (29) . . 129
30. Nikita Kuznetsov (30) . . . . 127
 
31. Ajit Athle (31). . . . . . . . . . . 126
32. Alan O'Donnell (32) . . . . . . 123
33. Claudio Baiocchi (34) . . . . 114
34. Fanfan (33) . . . . . . . . . . . . . 113
35. Akifumi Iwahashi (35) . . . . 108
35. Tim Nelson (35) . . . . . . . . . 108
37. Yakov Macak (37) . . . . . . 103
38. K Sengupta (38) . . . . . . . . . 96
39. Jayavel Sounderpandian (38) 94
40. Jon Stearn (40) . . . . . . . . . . 89
 
41. Prachai K.(41) . . . . . . . . . . 86
42. Drew (42) . . . . . . . . . . . . . . 85
43. Nats Kroy (45) . . . . . . . . . 80
43. Irina Kolesnik (43) . . . . . . 80
45. Steve Carlon (44) . . . . . . . 78
46. Ken Duisenberg (46) . . . . 76
47. Ravi Raja (47) . . . . . . . . . 74
48. Joao Sousa (48). . . . . . . . . 73
49. Filipe Gonçalves (49) . . . . 70
50. Etienne Desclin (50) . . . . 69
 
Rebecca Wooten . . . . . . . 62
Garry Malashkin . . . . . . 60
Al Nelson . . . . . . . . . . . . . 60
Zeke Moore . . . . . . . . . . . 59
Slanky . . . . . . . . . . . . . . . 56
Trevor Bird. . . . . . . . . . . 56
Gaurav Agrawal . . . . . . 55
Mario Roederer . . . . . . . 53
S. Khoo. . . . . . . . . . . . . . 51
Huan-yu Chung . . . . . . 51
 
Colleen Frye . . . . . . . . 48
Sarah DeSanctis. . . . . . 47
V Balakrishnan. . . . . . 46
Dave Seaman . . . . . . . 45
Kevin Williams. . . . . . 44
Oliver Schebanek . . . . 37
Mohamed Omar. . . . . 37
Greg Hess . . . . . . . . . . 35
Shinsuke Kuzuya. . . . 33
Omar Gymboski . . . . 31
Les Billig. . . . . . . . . . . 31
 
David Madfes . . . . . . 30
Danielle Janney. . . . . 30
Chen Sin Tak . . . . . . 29
Mahbubul Hasan . . . 27
Uwe Buenting . . . . . . 27
Derek Chin . . . . . . . . 27
Albert Alvarez . . . . . 24
Carl Chenard . . . . . . 24
Jeffrey Hunt . . . . . . . 24
David Stigant . . . . . . 23
Chris Pentacoff. . . . . 23
Andrew Bajunemi. . . 23
 
Coyotek . . . . . . . . . . . 22
AZ Runner . . . . . . . . 22
Michelle Lee. . . . . . . . 22
Guha Kaushik. . . . . . 22
Miao. . . =^o^= . . . . . 22
Joe Fendel . . . . . . . . 21
Doug Babcock. . . . . . 21
Rick Montgomery . . 20
Deborah Fradelis . . . 19
Adam Panagos . . . . . 19
Sam Wilson. . . . . . . . 19
 
Nic Hargreaves . . . . .18
Yu Chen Wang. . . . . 18
Moreau deSaint-Martin 17
Juan Carlos Carrara 17
Po-Nien Chen . . . . . . 17
Peter Williams . . . . . 17
Marcin Mika . . . . . . 16
Big Dave . . . . . . . . . . 16
Giridihar Prasannan 15
Payman Parang. . . . 15
Montta . . . . . . . . . . . 15
Cheryl Lim Xuanzi . 15
 
James Laverty . . . . . 14
Jin Won Park . . . . . 14
Thad . . . . . . . . . . . . . 14
Charles Lo . . . . . . . . 14
Tat Tsui. . . . . . . . . . . 14
Ji Zheng . . . . . . . . . . 13
Tim Boomer . . . . . . . 13
Chris North . . . . . . . 13
Jesse Goldlink . . . . . .13
Maria Pereira. . . . . . 13
Jeff O'Connell . . . . . 13
Jason M. McCargar. 13
 
b basic . . . . . . . . . . . . 12
Wanda Cahill . . . . . . 12
Troy Butler . . . . . . . . 12
Paul Botham . . . . . . 12
Pat Gremban . . . . . . 12
Steve Tonnesen. . . . . 11
Farid Mark Watson. 11
Dangkhoa Pham . . . 11
Matt Situ . . . . . . . . . 11
Kia Davidson . . . . . . 11
 
Frank Mullin . . . . . . 10
Ameya Joshi . . . . . . . 10
David Huang . . . . . . 10
Abbas Mehrabian . . 10
Navi Sidhu . . . . . . . . 10
Charles Stanton . . . . 10
Matt Rattigan. . . . . . 10
Kenneth Potstada. . . 10
Jen-Kai Pan . . . . . . . 10
James Layland. . . . . 10
Dave B. . . . . . . . . . . . 10
 
Dennis Molter . . . . . . . . 9
Yonlawan Chirawatcharadej 9
Rajwant Singh. . . . . . . . 9
Joon Sup. . . . . . . . . . . . . 9
 
Morandi Maurizio. . . . . 8
Wenjun Kang. . . . . . . . . 8
Monika Reynolds . . . . . 8
Ritwik Chaudhuri . . . . 8
Tim Bock . . . . . . . . . . . . 8
Katherine Dostal . . . . . . 8
Alex Chan . . . . . . . . . . . 8
Sabina Paradi . . . . . . . . 8
Punam Bhullar . . . . . . . 8
Nilesh Patel . . . . . . . . . . 8
Sarah Mahdavi . . . . . . . 8
 
Aclaira . . . . . . . . . . . . . . 7
Joe Schank. . . . . . . . . . . 7
Mark Moyer . . . . . . . . . . 7
Tom Esser . . . . . . . . . . . . 7
Tom Falbo. . . . . . . . . . . . 7
Kelly K. . . . . . . . . . . . . . . 7
Bernie Leitner. . . . . . . . . 7
Wilson Matheson . . . . . . 7
Jonathan Ediyanto. . . . . 7
 
Mark Moyer . . . . . . . . . . 6
Brady Wern . . . . . . . . . . 6
Adam Morgan . . . . . . . . 6
Sara Elsnick. . . . . . . . . . 6
Michael Thwaites. . . . . . 6
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Charleen Yen . . . . . . . . . 6
Martin Gritsch. . . . . . . . 6
Greg McWhirter. . . . . . . 6
Robert Hussey . . . . . . . . 6
Bruce. . . . . . . . . . . . . . . . 6
Kristen Hehr . . . . . . . . . 6
Monsan . . . . . . . . . . . . . 6
Miho Koto . . . . . . . . . . . 6
Brian Lin . . . . . . . . . . . . 6
Melina Hidayat . . . . . . . 6
Jessica Bubb. . . . . . . . . . 6
Maurice Turrieta. . . . . . 6
George Caleodis. . . . . . . 6
Flavio Cherarola . . . . . . 6
 
Haley Buxton. . . . . . . . . 5
Danny Roe. . . . . . . . . . . 5
Luis deBrito Camacho . 5
Eric Targowski. . . . . . . 5
Sumita Das. . . . . . . . . . 5
Mike Kosciuk. . . . . . . . 5
Robert Dostal . . . . . . . . 5
Jim No-Spam . . . . . . . . 5
Richard Hillman . . . . . 5
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Erin Keithley . . . . . . . . 5
Cindy Tang . . . . . . . . . 5
Richard Clarke . . . . . . 5
Amy Maris. . . . . . . . . . 5
Marowen Ng . . . . . . . . 5
Megan Spillane . . . . . 5
Ileen Huh . . . . . . . . . . 5
Esther Li. . . . . . . . . . . 5
Andy Harmon . . . . . . 5
Vvalker Kellogg. . . . . 5
Connie C. . . . . . . . . . . 5
Heather Jameson . . . . 5
 
Jeff Peterson . . . . . . . . 4
Damon Haught. . . . . . 4
Subba Ready . . . . . . . 4
Cliff Angle . . . . . . . . . 4
Gordon Berg . . . . . . . . 4
T Miller . . . . . . . . . . . . 4
Joel Haywood . . . . . . . 4
Shanthy Krishnamurthy . 4
(S.G.) Roy . . . . . . . . . . . 4
Albert Heinrich . . . . . 4
Sandy Thompson . . . . 4
Leora . . . . . . . . . . . . . . 4
Basem Chaikhouni . . 4
Anne Sufka . . . . . . . . . 4
Andy Hsieh . . . . . . . . . 4
Adam Levy . . . . . . . . . 4
Yvette Bitar . . . . . . . . . 4
Tu Truong. . . . . . . . . . 4
Cheryl Fredricks. . . . . 4
Lorenzo Grespan . . . . 4
Max Mojab . . . . . . . . . 4
Samuel McArthur . . . 4
Yuri Sumnicht . . . . . . 4
Nicole Hetzer . . . . . . . 4
Aaron Mikuni . . . . . . 4
Matt Whitlow . . . . . . 4
Cliff Young. . . . . . . . . 4
Kevin Marshall . . . . . 4
CRM . . . . . . . . . . . . . . 4
 
Ondrej Calda . . . . . . . 3
Dawn Haught . . . . . . . 3
JaeKon Lee . . . . . . . . . 3
Kyle Misiaszek . . . . . 3
Arijit Bhattacharyya . . 3
Tony Wang . . . . . . . . . 3
Mo Money . . . . . . . . . . 3
Stefan Gatachiu . . . . . 3
Ameya Mannikar . . . . 3
Abhijit Parashar . . . . 3
Hemingway. . . . . . . . . 3
Felix Chan. . . . . . . . . . 3
Michael Callahan . . . . 3
John Smith . . . . . . . . . 3
Nemesis Enforcer . . . . 3
Arijit Bhattacharyya. . . 3
Charlene Bong . . . . . . 3
Bob Seegmiller . . . . . . 3
Larry Corrado . . . . . . 3
Jerome Mahadeo . . . . 3
Ayane Buccini . . . . . . 3
OsmTechie . . . . . . . . . 3
Dan Carey . . . . . . . . . 3
Marc Wallace . . . . . . 3
Jeff Limber . . . . . . . . 3
Crystal Lai . . . . . . . . 3
Lindsay Dann . . . . . . 3
Myung Hwa Yang . . . 3
Chris Jones . . . . . . . . 3
Uri Andrews . . . . . . . 3
Sukhmine Bains . . . . 3
Tony Sun . . . . . . . . . . 3
Adel Farahmand . . . . 3
Gleb Podkolzin. . . . . 3
Willette . . . . . . . . . . . 3
Cristina Cancio . . . . 3
Yehuda Levy . . . . . . . 3
Martin Gritch . . . . . . 3
John DeLaurentis . . 3
George Perry . . . . . . . 3
Alison Muñoz . . . . . . 3
Joya Guha . . . . . . . . . 3
Richard Miller . . . . . 3
TripleVCourtois . . . . 3
Greg Silin . . . . . . . . . 3
Joseph Hendricks . . . 3
Carl Main . . . . . . . . . 3
Gohan . . . . . . . . . . . . 3
Daniel Cho . . . . . . . . 3
Warren Peace . . . . . . 3
Arthur Thung . . . . . . 3
Greg Vitan . . . . . . . . . 3
Hoodin Hamidi . . . . . 3
 
Riley Wern . . . . . . . . 2
Alex Kim . . . . . . . . . . 2
Art Wolfskill . . . . . . . 2
Bengt Blomster . . . . . 2
Oxana Urdaneta . . . . 2
Bob Chen . . . . . . . . . . 2
Jacket . . . . . . . . . . . . . 2
Isha Kotecha. . . . . . . . 2
Keith Downey. . . . . . . 2
Adam Ramage . . . . . . 2
Justin Bradley . . . . . . 2
David B. . . . . . . . . . . . 2
Sean Allaband . . . . . . 2
Rewon C . . . . . . . . . . . 2
Vallee Suennen . . . . . 2
Florian Fischer. . . . . . 2
Dan Greene . . . . . . . . . 2
Charlie Acquisio . . . . 2
Jason McConnell . . . . 2
Barry Thompson . . . . 2
Joe Skolnik . . . . . . . . . 2
Rich Futrell. . . . . . . . . 2
Peter Hendriks . . . . . . 2
Ben Cesch . . . . . . . . . . 2
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Heesoo Chang. . . . . . . . 2
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Dawn Snyder . . . . . . . . 2
--The Bozzball . . . . . . . 2+
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Santo . . . . . . . . . . . . . . 2
Andy Oats . . . . . . . . . . 2
David Nadler . . . . . . . . 2
Anandi (Rao) . . . . . . . . 2
Nick Sherrard . . . . . . . 2
Mahul Bhattacharya . 2
Pam Deutsch . . . . . . . 2
Gilad Skyte . . . . . . . . 2
Andy Oats. . . . . . . . . . 2
Joanne Dunlap . . . . . 2
Ravi Subramanian . . 2
Nemo Dumple . . . . . . 2
Bugz Podder. . . . . . . . 2
Erika Brandner . . . . . 2
Trevor Wells . . . . . . . 2
Paul Robinson . . . . . . 2
Ahearn Bizmah . . . . . 2
Marcel Birthelmer . . . 2
Musthaffa Kannipoyil 2
Jorge Ramirez. . . . . . . 2
Ernesto von Ruckert. . 2
Tai Dang . . . . . . . . . . 2
Mehdi Ansari . . . . . . 2
Mike Fuqua . . . . . . . . 2
Hareenda Yalamanchili 2
Michael Browell. . . . . 2
Jon Wilson. . . . . . . . . 2
Mercedes Foster . . . . . 2
Edwin Wijono . . . . . . 2
Conrad Tan . . . . . . . . 2
Daria Eiteneer. . . . . . 2
Matt Albrecht . . . . . . 2
Dan Lowenthal . . . . . 2
Default . . . . . . . . . . . . 2
P Ranger . . . . . . . . . . 2
John Trott . . . . . . . . 2
Katie Nechayev. . . . . 2
Jaewon Yoon . . . . . . 2
Exotic Nut . . . . . . . . 2
Branden Bedwell . . . 2
Kevin Ho . . . . . . . . . . 2
Quoctan Nguyen. . . . 2
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Jenee Donner . . . . . . 2
Tim Gavin . . . . . . . . 2
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Reyy . . . . . . . . . . . . . 2
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Truman Lee . . . . . . . 2
Tom DeSanctis . . . . . 2
Alix Erie . . . . . . . . . . 2
Camilo Jimenez. . . . 2
Nikki Carr . . . . . . . . 2
Triono Dawis . . . . . . 2
Chris Block . . . . . . . 2
AD/Marsha Reichle . 2
Kristy Poindexter . . . 2
Lisa Cassidy . . . . . . . 2
Aaron Murdock. . . . . 2
Candace Brant. . . . . . 2
 
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Hendrik van Eijsden 1
Mahul Bhattacharya. 1
Pee Wee . . . . . . . . . . . . 1
Jeff Olson . . . . . . . . . . 1
Polly Lau . . . . . . . . . . 1
Corey Ramsey . . . . . . 1
LetsGoCubs . . . . . . . . 1
Barb Owca . . . . . . . . . 1
Henry Yang. . . . . . . . . 1
Ralph Nguyen . . . . . . 1
Daniel Baczkowski . . 1
Debbie Miller . . . . . . 1`
Divyanshu Mishra . . 1
Abbey the Mathematician 1
Marisa Carcallas . . . 1
Barb G. . . . . . . . . . . . 1
Math 012378 . . . . . . 1
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vze4bwtf . . . . . . . . . . 1
Wait . . . . . . . . . . . . . 1
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Kathy Serbin . . . . . . 1
Dodopotpie . . . . . . . . 1
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Padmaja . . . . . . . . . . 1
Alex Shen . . . . . . . . . 1
Cyril Virtusio . . . . . 1
Erudite 1A . . . . . . . . 1
Dan Baczkowski. . . . 1
Manuel Fulea . . . . . . 1
Paul Langford. . . . . . 1
Aimee Jacot . . . . . . . . 1
Anthony Leung. . . . . 1
Cari Richardson. . . . 1
Anne Wood. . . . . . . . 1
Brita Groves . . . . . . . 1
Greg Hoggarth . . . . . 1
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Ji-Hong Min . . . . . . . 1
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Michael Williams. . . 1
Judy Kane. . . . . . . . . 1
XCute . . . . . . . . . . . . 1
L Mac. . . . . . . . . . . . . 1
Kimy Leung . . . . . . . 1
Gene Oldfield . . . . . . 1
B.M.W. . . . . . . . . . . . 1
Leo S. Bach. . . . . . . . 1
Kavita Aggarwal . . . 1
Randy Toy . . . . . . . . 1
T. Jackowski. . . . . . . 1
Pooboy . . . . . . . . . . . . 1
Zheng Shuwei. . . . . . 1
Rebecca Frye . . . . . . . 1
Kiyomi Sakata . . . . . 1
Utku Aksu . . . . . . . . 1
Erik Thompson. . . . . 1
Daniel Bonilla. . . . . . 1
Mike Birnbaum. . . . . 1
Cathy Bird . . . . . . . . 1
     
Previous Contest Standings 1997-2006
 
 
 
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Deadline for Problem #274 is Sun Mar 30, 2008 !
 
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